Understand the rights of an EU citizen and their non-EU family members to attain permanent residency (séjour permanent) status...

Any EU citizen who has been resident in France for five or more continuous years has the right to permanent residence and a residence permit and does not need to provide proof of income or employment. This also applies to citizens of the New EU accession countries. The time is reduced in some cases such as being a parent of a French national or being married to one.
A person may be required to prove the continuity of their residence in France over the five years; this can be proven by any means and is not altered by absences of up to six months per year or an absence of up to a year for reasons of illness, study or a professional posting elsewhere.
The right to permanent residence is lost after a person has not lived in France for more than two consecutive years.
The permanent residence permit "EU permanent stay all occupations" (UE séjour permanent, toutes activités professionnelles) is renewable. Acquiring this card is optional.

Non-EU family members permanent residence rights

Non-EU family members receive the right to permanent residence on the same criteria as their EU family if they have resided together in France for over five years. Application for the permanent residency card is obligatory, and must be made two months before the Carte de Séjour expires. The new permit, UE séjour permanent, toutes activités professionnelles must be renewed two months before expiry.
Non-EU citizens who have been granted a right to residence based on their marriage to an EU citizen retain that right in the event of divorce or death of their EU spouse.